Least Common Multiple (LCM) of 16 and 157
The least common multiple (LCM) of 16 and 157 is 2512.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 16 and 157?
First, calculate the GCD of 16 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 16 ÷ 157 = 0 remainder 16 |
| 2 | 157 ÷ 16 = 9 remainder 13 |
| 3 | 16 ÷ 13 = 1 remainder 3 |
| 4 | 13 ÷ 3 = 4 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 141 and 91 | 12831 |
| 153 and 48 | 2448 |
| 147 and 181 | 26607 |
| 107 and 158 | 16906 |
| 33 and 116 | 3828 |